lmomcau {lmomco} | R Documentation

## Trimmed L-moments of the Cauchy Distribution

### Description

This function estimates the trimmed L-moments of the Cauchy distribution given the parameters (xi and α) from `parcau`. The trimmed L-moments in terms of the parameters are

λ^{(1)}_1 = xi mbox{,}

λ^{(1)}_2 = 0.698α mbox{,}

tau^{(1)}_3 = 0 mbox{, and}

tau^{(1)}_4 = 0.343 mbox{.}

### Usage

    lmomcau(para)

### Arguments

`para` | The parameters of the distribution.

### Value

An R `list` is returned.

`lambdas` | Vector of the trimmed L-moments. First element is λ^{(1)}_1, second element is λ^{(1)}_2, and so on.
`ratios` | Vector of the L-moment ratios. Second element is tau^{(1)}, third element is tau^{(1)}_3 and so on.
`source` | An attribute identifying the computational source of the L-moments: “lmomcau”
`trim` | Level of symmetrical trimming used—`trim=1`.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Gilchrist, W.G., 2000, Statistical modeling with quantile functions: Chapman and Hall/CRC, Boca Raton, FL.

### See Also

`parcau`, `quacau`, `cdfcau`

### Examples

    X1 <- rcauchy(20)
    lmomcau(parcau(TLmoms(X1,trim=1)))

[Package lmomco version 0.92 Index]